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Mirrors > Home > ILE Home > Th. List > mobii | GIF version |
Description: Formula-building rule for "at most one" quantifier (inference form). (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 17-Oct-2016.) |
Ref | Expression |
---|---|
mobii.1 | ⊢ (𝜓 ↔ 𝜒) |
Ref | Expression |
---|---|
mobii | ⊢ (∃*𝑥𝜓 ↔ ∃*𝑥𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mobii.1 | . . . 4 ⊢ (𝜓 ↔ 𝜒) | |
2 | 1 | a1i 9 | . . 3 ⊢ (⊤ → (𝜓 ↔ 𝜒)) |
3 | 2 | mobidv 2062 | . 2 ⊢ (⊤ → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒)) |
4 | 3 | mptru 1362 | 1 ⊢ (∃*𝑥𝜓 ↔ ∃*𝑥𝜒) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 105 ⊤wtru 1354 ∃*wmo 2027 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-eu 2029 df-mo 2030 |
This theorem is referenced by: moaneu 2102 moanmo 2103 2moswapdc 2116 2exeu 2118 rmobiia 2666 rmov 2757 euxfr2dc 2922 rmoan 2937 2rmorex 2943 mosn 3628 dffun9 5245 funopab 5251 funco 5256 funcnv2 5276 funcnv 5277 fun2cnv 5280 fncnv 5282 imadif 5296 fnres 5332 ovi3 6010 oprabex3 6129 axaddf 7866 axmulf 7867 frecuzrdgtcl 10411 frecuzrdgfunlem 10418 fsum3 11394 |
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